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Transcript
Isospin effect in asymmetric nuclear matter (with QHD II model) Kie sang JEONG Effective mass splitting • from nucleon dirac eq. here energymomentum relation • Scalar self energy • Vector self energy (0th ) Effective mass splitting • Schrodinger and dirac effective mass (symmetric case) • Now asymmetric case visit • Only rho meson coupling • + => proton, - => neutron Effective mass splitting • Rho + delta meson coupling • In this case, scalar-isovector effect appear • Transparent result for asymmetric case Semi empirical mass formula • Formulated in 1935 by German physicist Carl Friedrich von Weizsäcker • 4th term gives asymmetric effect • This term has relation with isospin density QHD model • Quantum hadrodynamics • Relativistic nuclear manybody theory • Detailed dynamics can be described by choosing a particular lagrangian density • Lorentz, Isospin symmetry • Parity conservation * • Spontaneous broken chiral symmetry * QHD model • QHD-I (only contain isoscalar mesons) • Equation of motion follows QHD model • We can expect coupling constant to be large, so perturbative method is not valid • Consider rest frame of nuclear system (baryon flux = 0 ) • As baryon density increases, source term becomes strong, so we take MF approximation QHD model • Mean field lagrangian density • Equation of motion • We can see mass shift and energy shift QHD model • QHD-II (QHD-I + isovector couple) • Here, lagrangian density contains isovector – scalar, vector couple Delta meson • Delta meson channel considered in study • Isovector scalar meson Delta meson • Quark contents • This channel has not been considered priori but appears automatically in HF approximation RMF <–> HF • If there are many particle, we can assume one particle – external field(mean field) interaction • In mean field approximation, there is not fluctuation of meson field. Every meson field has classical expectation value. RMF <–> HF • Basic hamiltonian RMF <–> HF • Expectation value Hartree Fock approximation Classical interaction between one particle - sysytem Exchange contribution H-F approximation • Each nucleon are assumed to be in a single particle potential which comes from average interaction • Basic approximation => neglect all meson fields containing derivatives with mass term H-F approximation • Eq. of motion Wigner transformation • Now we control meson couple with baryon field • To manage this quantum operator as statistical object, we perform wigner transformation Transport equation with fock terms • Eq. of motion • Fock term appears as Transport equation with fock terms • Following [PRC v64, 045203] we get kinetic equation • Isovector – scalar density • Isovector baryon current Transport equation with fock terms • kinetic momenta and effective mass • Effective coupling function Nuclear equation of state • below corresponds hartree approximation • Energy momentum tensor • Energy density Symmetry energy • We expand energy of antisymmetric nuclear matter with parameter • In general Symmetry energy • Following [PHYS.LETT.B 399, 191] we get Symmetry energy nuclear effective mass in symmetric case Symmetry energy vanish at low densities, and still very small up to baryon density • reaches the value 0.045 in this interested range • • Here, transparent delta meson effect Symmetry energy • Parameter set of QHD models Symmetry energy • Empirical value a4 is symmetry energy term at saturation density, T=0 When delta meson contribution is not zero, rho meson coupling have to increase Symmetry energy Symmetry energy • Now symmetry energy at saturation density is formed with balance of scalar(attractive) and vector(repulsive) contribution • Isovector counterpart of saturation mechanism occurs in isoscalar channel Symmetry energy • Below figure show total symmetry energy for the different models Symmetry energy • When fock term considered, new effective couple acquires density dependence Symmetry energy • For pure neutron matter (I=1) • Delta meson coupling leads to larger repulsion effect Futher issue • • • • • Symmetry pressure, incompressibility Finite temperature effects Mechanical, chemical instabilities Relativistic heavy ion collision Low, intermediate energy RI beam reference • • • • • • Physics report 410, 335-466 PRC V65 045201 PRC V64 045203 PRC V36 number1 Physics letters B 191-195 Arxiv:nucl-th/9701058v1